Big Idea: Observation and description of changes in the world around us are
the first steps in finding and learning about patterns.
INV 3 Essential Question: How can I visually explain situations where one thing changes based on another?
Problem 3.1- Renting Bicycles
A) Q: Which Bike shop should Ocean and History Bike Tours use? Explain your choice.
A: The Ocean and History Tours should rent bikes from Adrian's bike shop if they are renting 0-35 bikes. This is because Adrian's Bike Shop's prices increases at about $150.00 each extra 5 bikes, the prices are reasonable (cheaper than Rocky's Cycle Center). If Ocean and History Tours wants to rent 40+ bikes, they should rent their bikes from Rocky's Cycle Center. This is because their prices start expensive and as you rent more bikes, they give a bigger discount. Basically, the more bikes you rent, the more discount they give you at Rocky's Cycle Center, unlike Adrian's bike shop, which gives about (median of data) $150.00 each extra 5 bikes rented.
B) Q: Explain how you used the information in the table and the graph to make your decision.
A: I found the differences between all of the same '# of bikes' intervals from the graph (Adrian's bike Shop) and the table (Rocky's cycle Center). Then I compared the prices at each interval of '# of bikes' to make my decision/conclusion.
Adrian's Bike Shop Graph
of bikes
0
5
10
15
20
25
30
35
40
45
50
Rental fee ($)
0
400
535
655
770
875
975
1070
1140
1180
1200
Rocky's Cycle Center Rental fee
Problem 3.1- Renting Bicycles Follow up
1) Q: In the graph from Adrian's Bike Shop, would it make sense to connect the points with a line? Why or Why not?
A: Yes, it would make sense to connect the dots on the graph for. If the information in the graph about renting bikes were continuous, it would make sense to connect the points, to show the pattern clearer. It makes it much easier to recognize the number patterns if you connect the dots.
2) Q: How much do you think each company would charge to rent 32 bikes?
A: For Rocky's Cycle Center, I think it will cost around $1013.00 to rent 32 bikes, because that is the median between intervals '# of bike' 30-35.
For Adrian's Bike Shop, I think it will cost around $950.00 to rent 32 bikes, because that is the median between intervals '# of bike' 30-35. 3) Q: Look for patterns on page 37. For each display, describe in words the pattern of change in data.
A:
Rocky's Cycle Center table patterns: First it starts with a very expensive price ($400.00), then keeps dropping as it goes on adding more money as you keep renting more bikes. The discount increases slow at first (it increases in 5 or 10 more ($) each 5 more bikes rented), then it starts to increase faster (keep adding 5/10 more ($) discount each time for each more 5 bikes rented/rentable), then eventually drops tremendously (keep adding 30/35 ($) more discount each time 5 more bikes rented/rentable), until eventually the price becomes 0 or even they start paying you back if the fee for renting bikes goes on in the same pattern.
Adrian's Bike Shop graph patterns: It starts and keeps adding around (10, 20 or 30 dollars under or over) $150.00 every extra 5 bikes, making the price eventually extravagant, and too expensive for that quantity of bikes if you follow this pattern.
4) Q: Based on patterns you found in q. 3, how can you predict values that are not included in the table or graph?
A: If you want to predict the prices of 50+ bikes, Rocky's Cycle Center would keep dropping the # of $'s that they add to the price (each extra 5 bikes being rented), that eventually, the price would start going down instead up and they would eventually start paying you. For Adrian's Bike Shop, if you wanted to know 50+ bikes' prices, just keep adding about $150.00 to each 5 extra bikes rented.
Sept. 13/09
Math 7B
Big Idea:
Observation and description of changes in the world around us are
the first steps in finding and learning about patterns.
INV 3 Essential Question: How can I visually explain situations where one thing changes based on another?
Problem 3.1- Renting Bicycles
A) Q: Which Bike shop should Ocean and History Bike Tours use? Explain your choice.
A: The Ocean and History Tours should rent bikes from Adrian's bike shop if they are renting 0-35 bikes. This is because Adrian's Bike Shop's prices increases at about $150.00 each extra 5 bikes, the prices are reasonable (cheaper than Rocky's Cycle Center). If Ocean and History Tours wants to rent 40+ bikes, they should rent their bikes from Rocky's Cycle Center. This is because their prices start expensive and as you rent more bikes, they give a bigger discount. Basically, the more bikes you rent, the more discount they give you at Rocky's Cycle Center, unlike Adrian's bike shop, which gives about (median of data) $150.00 each extra 5 bikes rented.
B) Q: Explain how you used the information in the table and the graph to make your decision.
A: I found the differences between all of the same '# of bikes' intervals from the graph (Adrian's bike Shop) and the table (Rocky's cycle Center). Then I compared the prices at each interval of '# of bikes' to make my decision/conclusion.
Problem 3.1- Renting Bicycles Follow up
1) Q: In the graph from Adrian's Bike Shop, would it make sense to connect the points with a line? Why or Why not?
A: Yes, it would make sense to connect the dots on the graph for. If the information in the graph about renting bikes were continuous, it would make sense to connect the points, to show the pattern clearer. It makes it much easier to recognize the number patterns if you connect the dots.
2) Q: How much do you think each company would charge to rent 32 bikes?
A: For Rocky's Cycle Center, I think it will cost around $1013.00 to rent 32 bikes, because that is the median between intervals '# of bike' 30-35.
For Adrian's Bike Shop, I think it will cost around $950.00 to rent 32 bikes, because that is the median between intervals '# of bike' 30-35.
3) Q: Look for patterns on page 37. For each display, describe in words the pattern of change in data.
A:
4) Q: Based on patterns you found in q. 3, how can you predict values that are not included in the table or graph?
A: If you want to predict the prices of 50+ bikes, Rocky's Cycle Center would keep dropping the # of $'s that they add to the price (each extra 5 bikes being rented), that eventually, the price would start going down instead up and they would eventually start paying you.
For Adrian's Bike Shop, if you wanted to know 50+ bikes' prices, just keep adding about $150.00 to each 5 extra bikes rented.